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Buckingham π theorem states that an equation involving n number of
physical variables which are expressible in terms of k independent fundamental
physical quantities can be expressed in terms of p = n - k dimensionless
parameters.

To start with a very simple case, consider that you want to find a dimensionless
quantity involving the magnitudes V, T and L with dimensions [length]/[time],
[time] and [length] respectively.

What is the pressure loss p in a pipe with length L and diameter D for a fluid with density d, and viscosity m travelling with speed v? As pressure, mass, volume, viscosity and speed are defined as derived dimensions in the registry, we only need to explicitly write the density dimensions.